To record yoga classes with good video quality, I would recommend a camera that combines a good optical zoom and recording capabilities in low light conditions. Additionally, it would be ideal if it has a versatile mounting system so you can easily set it up.
As for the equipment, many advanced security cameras offer features such as motorized zoom, stability in recordings, and ease of connection to other devices, which could be useful for your live classes. Although they are primarily designed for surveillance, some of these cameras offer excellent video quality and are easy to set up in different environments, making them a very valid option for what you need. I got mine for something similar:
https://chicagosecuritypros.com/
Also, make sure the camera has HDMI output or another method of connection to your laptop, as this will make it easier to record your sessions in real-time.
I hope you find the perfect camera for your needs, and that your classes are a great success!